How old is this tank?
Was it started with live rock?
Uronema is not an obligate parasite....the highly disturbed conditions of the tank caused them to turn to the fish for sustenance. The immune systems of the fish in question were probably low-functioning as a result of the same issues.
IMO, you shouldn't have to sterilize the tank....that might even be counter to the long term effort of stability.
Uronema marinum are normally free-living bacteria eaters – harmless to your fish.
Making sure your tank is matured enough for the fish being added. And make sure the fish get a freshwater dip before going into the display. With that you should be quite unlikely to have problems again.
As the link indicates, the fish that "have it worse" than what a freshwater dip will fix already have a poor prognosis...meaning they're unlikely to make it no matter what you do. This does happen, but should be extremely rare. Freshwater dips are a pretty strong screen. Uronema is almost unheard of, even among the crowds that do tend to have sick fish at the beggining of their tank.
IMO, shift into a slower gear, start the tank up with just some minor cleanup crew, and if you don't have corals you can even take it back to dark. Let it grow in this way for a few months. Don't let the tank starve, but don't to any big feedings during this period. After it's been calm, try lights and a few coral. Make sure you keep up with any algae growth...and add CUC as needed
to help you.
Once that seems stable and you feel on top of the algae cycles, etc, you can start adding fish....I'd start with one and let that ride for a few months until you've seen the cycles come and go....then add some more corals....wait....a few more fish....wait.....etc. It should take quite a while to fill up a tank with fish.
(apparently there's a green algae with the identical name of our cilliate....isn't that not supposed to happen??? LOL)